This invention relates to the field of nonlinear controllers and is particularly adapted to augment conventional Proportional-Integral-Derivative (PID) controllers function more effectively for controlling time varying dynamic processes and systems.
Controllers are inherently complex since they control dynamically changing systems, trying to match a desired response with the system output. (The desired response can be a setpoint change or the output curve of a reference model exhibiting the desired response characteristics. In most real control situations, one would not expect, and cannot achieve, the process output being brought to setpoint instantaneously. Therefore, following the presumed optimal curve is the goal.)
Both by virtue of and despite their simplicity, linear controllers continue to be the workhorse of control applications. In particular, the vast majority of current applications employ proportional-integral-derivative (PID) controllers. In the aerospace as well as process industries, PID control has proven to be easy to use and to provide adequate performance. PID controllers are also general purpose, that is, the same controller structure can be used for a broad range of applications.
Yet PID control is far from ideal. For any nontrivial application, we know that nonlinear controllers can substantially outperform a PID. For specific plants, high-performing nonlinear controllers can be designed. But, in practice, this has required unique designs for each enterprise, with concomitant high cost and complexity. At this time there is no formal approach for developing general nonlinear controllers.
We have developed a "NeuroPID Controller" concept that is a potential solution to this problem which employs a neural network to realize a nonlinear controller but retains the PID interface.
Thus, it exhibits the easy to use and application-independent properties of conventional PID controllers, while utilizing the nonlinear dynamical system modeling properties of neural networks to realize control laws that are more robust, accurate, and generalizable to applications than other approaches.
PID controllers are used ubiquitously for conventional controls. As conventionally formulated, these PID controllers use six input signals to generate an output to drive the plant process. The inputs are signals which represent on the one hand, controller parameters (or gains) K.sub.C, K.sub.I and K.sub.D and, on the other, three error signals: the error between the setpoint or reference model response and the process response, e, the integral of this error, .intg.e, and the derivative of this error, e. This function computed by conventional PID controllers is a linear weighted sum of the error signals: EQU u.sub.PID =K.sub.C e+K.sub.I .intg.e+K.sub.D e
It may be computed either in analog or digital fashion to yield u.sub.PID.
K.sub.C, K.sub.I, and K.sub.D are controller parameters, or gains. Their values uniquely determine controller output. In the conventional PID paradigm, it is assumed that by increasing the proportional gain K.sub.C, we can increase the closed loop bandwidth (reducing the time needed to attenuate disturbances); by increasing the derivative gain K.sub.D we can increase the damping (reducing overshoot): and by increasing the integral gain K.sub.I we increase the system robustness (reducing sensitivity to disturbances) and reduce steady-state tracking errors. The behavior of the closed loop system (dynamic system), however, does not always decouple in this way. That is, increasing integral gain may reduce damping, or increasing proportional feedback can increase sensitivity, etc. In practice, the user installs a PID controller box in a feedback loop and adjusts the gains until the closed loop response of the system is a good compromise among the user's competing objectives.
There is no theoretical reason to believe that this is the optimal function of these six quantities and, in fact, it is unlikely to be the optimal function especially in a large search space of possible nonlinear functions. Therefore, conventional PID controllers are not as good as they could be if the correct nonlinear function were applied to the PID control parameters. This invention shows two approaches to produce more effective PID controllers that can introduce nonlinear functions into the conventional PID paradigms. In addition, because of the identical interface with the conventional PID, much of the "jacketing software" implemented with many PID installations (e.g., anti-reset-windup, bias offset) is directly applicable to the NeuroPID. Our approach to dynamic neural networks has allowed us to use general connectivity patterns and associates dynamics with processing elements. In other words, neural networks that have dynamic elements whose outputs are fed back into the network, can be used to allow for accurate neural network modeling representation of dynamic systems. Therefore, not only can linear systems be controlled with neural network based controllers but, in particular, nonlinear dynamic systems can as well. As we demonstrate below, PID parameters can be used to effectuate this control.
A NeuroPID may be used in industrial plant control, and environmental control situations, as well as flight control. For example, in the flight control domain, the NeuroPID is advantageous for several reasons:
In the flight control domain, relatively simple controllers are essential in certain applications. Sophisticated model-based controllers, for example, cannot satisfy the computational constraints imposed by small flying systems. The memory and processing resources required by NeuroPID controllers are more than for conventional PIDs, but well within these constraints, even for software implementations. PA0 A well established approach to designing PID-based flight controllers exists. This same approach, or a simplified version of it, could be used for developing NeuroPID flight controllers. Gain scheduling can be used with the NeuroPID just as with PID control. PA0 Reasonably accurate aircraft models are available to be used during the design process. PA0 In principle, existing systems can even be retrofitted with NeuroPID controllers with minimal effort.